
where \(\chi \)  [1]} is the pair correlation function, \(\xi ^2_{0x}\)  and \(\xi ^2_{0y}\)  are the variance or strengths of the white noise along the \(x\) - and \(y\) -directions respectively and the collision integral \(I(f,f)\)  is given by
\(I(f,f)=\sigma \int d {v}_2 \int d {e} \Theta (-{v}_{12}.{e}) |{v}_{12}.{e}| \Big [ \frac{1}{r^2} f(v^{^{\prime \prime }}_1,t) f(v^{^{\prime \prime }}_2,t) - f({v}_1,t) f({v}_2,t) \Big ]. \) 
